PROBLEM $4$

Consider the thermal mixing process shown in the figure below. The level $(h)$ and the temperature $(T)$ are to be controlled by adjusting the flow rates of the hot and cold streams, $F_h$ and $F_c.$ The disturbance variables are the temperature of the inlet streams $T_h$ and $T_c.$ The outlet flow rate $F$ is maintained constant. Derive the transfer function matrix of the process. Represent the block diagram of that matrix.